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Person $A$ has information partition $\{\{1,2\},\{3,4\},\{5,6\}\}$

Person $B$ has information partition $\{\{1\},\{2,3\},\{4,5\},\{6\}\}$

$w=3$ has been realized.

I'm confused about what $A$ knows that $B$ knows.

At first I thought of it as $K_aK_b(3)=K_a(\{2,3\})=\{1,2,3,4\}$, but the example I found online says $K_aK_b(3)=\{2,3,4,5\}$. why?

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The situation is not described by $K_A(K_B(3))$. $A$ does not know that the draw was 3, and hence does not know that $B$ thinks it is in the set $K_B(3)$. What $A$ does know is that the draw is in set $K_A(3)$, hence $A$ thinks $B$ should have narrowed it down to $K_B(K_A(3))$.

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